Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C349 ⋊ C2 |
| Sylow | C349 ⋊ AGL(1,ℤ/8) |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,349|d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^348,d^b=de,f^b=f^3481751 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36374313, #36374314, #36374318, … |
| maximal normal subgroup of | #36374313, #36374314, #36374318, … |
| maximal quotient of | #36374146, #36374150, #36374186, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 174);